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Vertices: ; foci:

Ask by Davey Barrett. in the United States
Mar 18,2025

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The equation of the ellipse is .

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The Deep Dive

Did you know that the given vertices and foci represent a hyperbola? In this case, the vertices (0, ±8) indicate that the hyperbola opens vertically, as they lie on the y-axis. The distance from the center to the vertices shows the distance of 8 units, while the foci at (0, ±4) tell us that the hyperbola’s shape is defined by the relationship between the distance to the foci and the vertices, adhering to the hyperbola equation .
If you’re looking to sketch this hyperbola, start with plotting the center, which in this case is at the origin (0,0). From there, mark the vertices at (0, 8) and (0, -8). Then, plot the foci at (0, 4) and (0, -4). Finally, remember that the branches of the hyperbola will curve outward from each vertex, getting closer towards the foci but never touching them. This will give you a nice visual representation of this fascinating curve!

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